Experimental Proof of the Reciprocal Relation Between Spin Peltier and Spin Seebeck Effects in a Bulk YIG/Pt Bilayer

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OPEN Experimental proof of the reciprocal relation between spin Peltier and spin Seebeck efects Received: 4 October 2018 Accepted: 8 January 2019 in a bulk YIG/Pt bilayer Published: xx xx xxxx Alessandro Sola 1, Vittorio Basso1, Michaela Kuepferling1, Carsten Dubs 2 & Massimo Pasquale 1

We verify for the frst time the reciprocal relation between the spin Peltier and spin Seebeck efects in a bulk YIG/Pt bilayer. Both experiments are performed on the same YIG/Pt device by a setup able to accurately determine heat currents and to separate the spin Peltier heat from the Joule heat background. The sample-specifc value for the characteristics of both efects measured on the present YIG/Pt bilayer is (6.2 ± 0.4) × 10−3 KA−1. In the paper we also discuss the relation of both efects with the intrinsic and extrinsic parameters of YIG and Pt and we envisage possible strategies to optimize spin Peltier refrigeration.

Te reciprocal relations of thermodynamics are a fundamental tool to analyze and understand the physics of transport phenomena1. Since the beginning of the 19th century it was clear to Jean Charles Athanase Peltier and later demonstrated by Lord Kelvin, that for a material at a given absolute temperature T a relation exists between the Seebeck coefcient ε (given by the ratio between the measured electromotive force and the applied temperature diference) and the Peltier coefcient ∏ (the ratio between the measured heat current and the applied electric current): ∏ = εT 2,3. Tis remarkable reciprocity was later found to be part of a wider set of relations, as theoret- ically demonstrated by Onsager under the assumption of the reversibility of the microscopic physical processes governing macroscopic non-equilibrium thermodynamic efects4. Reciprocal relations can also be used to analyze transport phenomena which involve not only the electric charge and the heat, but also the spin. Spincaloritronic phenomena5–7 can provide additional tools to the feld of spintronics, envisioned to be a faster and lower energy consuming alternative to classical electronics8. One of the key building blocks for “spintronic circuits” is the spin battery, a device which can drive a spin current into an external circuit. Spin batteries are fundamental for spintronic devices and may be developed exploiting spincaloritronic efects9. Spincaloritronic devices may also be used in the development of novel thermoelectric heaters/ coolers operating at the microscale10,11. Te idea of a reciprocity between heat and spin was initially proposed and proven for metals where the spin current is carried by electrons12, but such a reciprocal relation cannot be easily proven in the case of ferrimagnetic insulators where the spin current is carried by thermally excited spin waves13. A typical device, where spincaloritronic efects are found and can be exploited for experiments, is a bilayer made of a ferrimagnetic insulator (e.g. yttrium iron garnet, YIG) and a non magnetic metal with a strong spin-orbit coupling (e.g. platinum, Pt)14. In these devices the spin current is generated longitudinally (along the x axis), normal to the flm surface. In the case of devices which exhibit the spin Peltier efect (SPE) a longitudinal (x axis) heat current is generated, caused by the fow of a transverse (y axis) electric current in the Pt layer13. Conversely, in the case of the spin Seebeck efect (SSE) a transverse (y axis) electric voltage is generated in the Pt layer and caused by the longitudinal temperature gradient parallel to the spin current (x axis)15. Although experimental evidence of both efects has been already obtained16,17, the quantitative demonstration of their reciprocity and the connection with intrinsic properties of the layers, has yet to be proven13,18–20. To this end here we provide the frst experimental evidence of the reciprocal relation between the thermal and the electric quantities associated to the SPE and the SSE in a bulk YIG/Pt bilayer. Te relation for a YIG/Pt bilayer has the following form21,22

1Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy. 2INNOVENT e.V., Technologieentwicklung, Prüssingstrasse. 27B, 07745, Jena, Germany. Correspondence and requests for materials should be addressed to A.S. (email: [email protected])

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Figure 1. (a) Geometry of the YIG/Pt bilayer with tYIG = 0.545 mm, Ly = 4.95 mm, Lz = 3.91 mm and tPt = 5 nm. (b,c) schemes of the device in the SPE and SSE confgurations. Heat currents and magnetic moment currents are along x (longitudinal direction), electric efects are along y (transverse direction), the magnetic feld and the magnetization are along z. (d,e) sketches of the experimental setup for SPE and SSE, respectively. (f) Experimental result of the SPE heat current, −Iq,SP , as function of the electric current Ie,y at positive magnetic saturation. (g) Experimental result of the SSE voltage ΔVe,y as function of the heat current Iq,x at positive magnetic saturation.

−Δ T ΔVe,y SP,x = T Ie,y Iq,x (1)

Te lef hand side of Eq. (1) refers to the SPE: ΔTSP,x is the temperature diference generated across the YIG layer as consequence of the electric current Ie,y fowing in the Pt flm. Te right hand side of Eq. (1) refers to the SSE: ΔVe,y is the voltage drop across the Pt flm caused by the heat current Iq,x fowing across the device and T is the average temperature of the YIG. Te experiments are performed measuring the SPE and the SSE on the same YIG/Pt device. Te experimental value which represents, within the uncertainty, both the SPE and the SSE response of the specifc device is (6.2 ± 0.4) × 10−3 KA−1. Results Device geometry and measurement principle. Te geometry of the bulk YIG/Pt bilayer is shown in Fig. 1a. Te device is composed of a bulk YIG parallelepiped with a thin flm of Pt sputter deposited on one side. Te temperature gradient ∇xT and the heat current density jq,x are directed along the x axis. Te electric voltage ΔVe,y and the electric current density je,y are directed along the y axis. Te magnetic moment current density, jM, is along the x direction and transports magnetic moments directed along the z direction. Te magnetic feld H and the magnetization M of the bulk-YIG are also directed along the z axis (Fig. 1b,c). Te measurement setup for both SPE and SSE is shown in the sketches of Fig. 1c,e. Te YIG/Pt device is sandwiched between two thermal reservoirs (held at Th and Tc respectively) in order to form a closed thermal circuit. Te temperature of the two reservoirs can be externally controlled and the two heat currents between the device and each of the reservoirs are measured simultaneously by sensitive heat fux detectors. Te heat fux technique is chosen to avoid measurement uncertainties due to the hardly reproducible thermal contacts23–26. In order to minimize heat leakages in the thermal circuit, the whole setup is operated in vacuum. Technical, constructional and measurement details are reported in the Methods section.

Spin Peltier efect. In the SPE, an electric current Ie,y fowing in the Pt layer generates a magnetic moment 27 current jM along the x direction as a result of the spin Hall efect . Te adjacent ferrimagnetic bulk YIG acts as a passive component and shows a longitudinal (x axis) heat current associated to the magnetic moment current injection28–30. Te measured heat current is however also including the Joule heat contribution generated by the electric current fowing in the Pt layer. In order to separate the Joule and spin Peltier contributions, their intrinsic diferences have to be exploited: the spin Peltier signal increases linearly with the Ie,y current and changes sign when the magnetization (along the z axis) or the Ie,y are inverted (odd parity), while Joule heating is proportional 2 13,18 to Ie,y and does not change sign under an inversion (even parity) . Te thermal problem of the SPE can be represented by the equivalent circuit of Fig. 2 (see also Supplementary material).

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Figure 2. Equivalent thermal circuit of the SPE measurements of the YIG/Pt bilayer. Te YIG layer is represented by the SPE generator, ΔTSP , and by the thermal resistance YIG. Te Pt layer has a Joule heat current source, Iq,JH, and a thermal resistance Pt. Te circuit includes two thermal contact resistances cont,c and cont,h taking into account both the thermal resistance of the contacts and the presence of the heat fux sensors. Te diference Iq,h − Iq,c = Iq,JH provides the Joule heat. In isothermal conditions, with Th = Tc = T, we have Δ=TISP q,sq+−I ,JHh()c /2 where hP=+tY/2 IG + cont,h, cc=+ont,cPt/2, Iq,s = (Iq,h + Iq,c)/2 is the half sum and  =+hc is the total resistance (see Supplementary material).

In adiabatic conditions the SPE corresponds to the direct measurement of ΔTSP , the temperature diference generated between the two faces of the bulk YIG sample. Previous experimental works have succeeded to 13,18 extract ΔTSP out of the Joule heat component by using an AC technique . Here, to test the reciprocal relation in a stationary state, we employ a DC technique in which we set isothermal conditions at the thermal baths, Th = Tc = T, and measure simultaneously the two heat currents: Iq,c and Iq,h. Te diference of the heat fux signals Iq,h − Iq,c = Iq,JH provides the Joule heat only (see Fig. 3a), while the half sum Iq,s = (Iq,h + Iq,c)/2 contains the SPE signal (see Fig. 3b,c). We frst detect the SPE generated by setting a constant electric current (i.e. Ie,y = 40 mA, see Fig. 3b, orange points) and periodically inverting the magnetic feld. Te half sum signal Iq,s has a change of ±2Iq,SP at each inversion. Equivalently, when the sign of the electric current in the Pt flm is changed (i.e. Ie,y = −40 mA, Fig. 3b, purple points), a sign inversion of the change 2Iq,SP occurs. Te feld inversion allows to detect the small contribution of the spin Peltier heat current (a few μW) superimposed to the Joule heating background (a few mW). As a second step we measure the SPE signal Iq,s at the constant magnetic feld μ0Hs = +50 mT while the applied current Ie,y = ±40 mA is periodically inverted, Fig. 3c, orange points. Conversely when we apply μ0Hs = −50 mT and the applied current Ie,y = ±40 mA is inverted, we obtain the curve of Fig. 3c, purple points. Te current inversion method provides the same results, within the uncertainty, as the magnetic feld inversion one, provided one takes into account the presence of small spurious ofset signals as discussed in the Methods section. Tis second method allows to detect the SPE signal as function of the applied magnetic feld. Terefore it permits the determination of the hysteresis loop of YIG31 (more details about this experiment are reported in Supplementary materials). At the saturating magnetic feld μ0Hs = +50 mT, by applying diferent values of Ie,y and by deriving the corresponding values of −Iq,SP as shown in Fig. 3b,c, we are able to obtain the linear relation between the SPE heat current and the electric current data of Fig. 1f. By a linear ft we fnd

−Iq,SP =.(5 10±.3) × 10−−51WA Ie,y (2) Te thermal resistance  of the whole stack consisting of sensors, sample and additional thermal contacts (e.g. thermal paste or thermally conducting layers) is experimentally measured by setting a heat current value and measuring the temperatures of the two thermal reservoirs by two thermocouples. Te result is  =±(119 2) KW−1. With Δ=TISP  q,SP, the measured spin Peltier coefcient is −ΔT SP =.(6 10±.4) × 10−−31KA Ie,y (3)

and since the current density fowing in the Pt flm is je,y = Ie,y/(tPtLz) with Lz = 3.9 mm and tPt = 5 nm we are fnally able to obtain the intrinsic SPE coefcient:

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Figure 3. Heat current signals measured on the YIG/Pt bilayer during the SPE experiment. (a) Joule heat signal given by the diference Iq,JH = Iq,h − Iq,c. (b) SPE by magnetic feld inversion. Half sum signal Iq,s = (Iq,h + Iq,c)/2 caused by a rectangular waveform of the magnetic feld |μ0Hs| = 50 mT, for two steady values of electric current (±40 mA, orange/purple). (c) SPE by electric current inversion. Iq,s caused by a rectangular waveform of the electric current |Ie,y| = 40 mA, for two steady values of magnetic feld (±50 mT, orange/purple). In both cases the spin Peltier signal Iq,SP is obtained as half of the variation at the inversion Iq,SP = ΔIq,s/2. Te variation ΔIq,s is taken at the inversion instant and is computed from the extrapolation of the linear ft taken a few seconds afer the inversion. Tis method permits to avoid the contributions of spurious induced voltage spikes afer the inversions. Te values reported in Fig. 1f) are the result of the average of 10 inversions.

−ΔT SP =.(1 19 ±.0 08) ×.10−−13 Km21A je,y (4)

Spin Seebeck efect. In the SSE experiment the bulk YIG is the active layer which generates a magnetic moment current when subjected to a temperature gradient, while the Pt is the passive layer in which the injected magnetic moment current is converted into a transverse electric potential. Te SSE signal measured across the Pt flm ΔVe,y changes sign when the magnetization of the YIG is inverted in sign (odd parity). Te measurement of the SSE is performed by setting a value of the heat current Iq,x traversing the YIG/Pt device and measuring the consequent voltage ΔVe,y found on the Pt layer when the YIG layer is at magnetic saturation. Te set of values obtained ΔVe,y versus the heat current Iq,x is shown in Fig. 1f and a linear ft gives ΔV e =.(2 10±.1) × 10−−51VW Iqx, (5)

A geometry independent (intrinsic) spin Seebeck coefcient can be defned as ∇yVe/jq,x with ∇yVe = ΔVe/Le,y and jq,x = Iq,x/Aq with Aq = Le,y × Lz. With Le,y = 4.17 mm, the dimension of the Pt electrode used to detect the voltage drop, and Lz = 3.91 mm we have

∇yeV =.(8 20±.3) × 10−−81VmW jqx, (6)

Finally the spin Seebeck coefcient SSSE = ∇yVe/∇xT, given by the ratio between the transverse gradient of the electric potential ∇yVe in Pt and the longitudinal gradient of the temperature ∇xT in YIG (as it is ofen defned in literature) can be obtained ∇ yeV −−71 SSSE =− κYIG =−(5.±40.×2) 10 VK jqx, (7)

−1 −1 32 using the bulk value of the thermal conductivity of YIG: κYIG = 6.63 Wm K . Tis result concurs with another −7 −1 33 experimental bulk YIG |SSSE|× 410 VK . Discussion Te microscopic and physical origin of the spin Peltier and of the spin Seebeck efects has been investigated in det ail26,28–30,34–43. Tese two efects are the results of two independent physical mechanisms. In YIG the presence of a spin current or, more generally, of a magnetic moment current, carried by thermally excited spin waves, is accom- panied by a heat current. In Pt the longitudinal spin polarized current is associated with a transverse electric efect due to the inverse spin Hall efect, described by the spin Hall angle θSH. At the interface between YIG and Pt the spin current is partially injected from one layer into the other44,45. By adopting the thermodynamic description of Johnson and Silsbee46 further developed in refs21,22,28–30, the thermomagnetic efects in YIG are described by means of the thermomagnetic power coefcient εYIG, that has an analogous role to the thermoelectric power coefcient ε of thermoelectrics. At the interface, the passage of the magnetic moment current, due to difusion, is mainly determined by the magnetic moment conductances per unit surface area, vM, of the two layers. Basing

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on these ideas, it has been possible to work out the reciprocal relation relating the spin Seebeck and spin Peltier efects with the intrinsic and extrinsic parameters of the bilayer. Te expression is21,22

−Δ T 11∇yeV μ  εσ SP = t = θμ B  YIGYIG Pt SH 0  κ jTe jqx, evp YIG (8) Eq. (8) contains two equal signs. Te equal sign at the lef is between the SPE and SSE measured quantities and we fnd the temperature diference between the two faces of YIG, ΔTSP, of the SPE generated by the electric current density je,y and the transverse gradient of the electric potential in Pt, ∇yVe, of the SSE, generated by the heat current density, jq,x, in YIG. Te equal sign at the right refers to the relation of both SPE and SSE to intrinsic coefcients. In addition to the expected parameters: θSH, the spin Hall angle of Pt and εYIG, the thermomagnetic power coefcient of YIG, we have: σYIG, the magnetic moment conductivity of YIG, vp, the magnetic moment conductance per unit surface area of the YIG/Pt interface and κYIG, the thermal conductivity of the YIG. μ0 is the magnetic constant, μB is the Bohr magneton and e is the elementary charge. vp depends on the intrinsic conductances, vM of both YIG and Pt and on the ratio t/lM between the thickness t and the magnetic moment difusion 22 length lM, for each layer. Te expression of vp is derived in ref. and reported in the Supplementary material. By just taking the frst equal sign of Eq. (8) and integrating over the size of the bilayer device we have Δ −Δ TSP 1 VLey,,/ qy = tPt ILey,z/( ⋅ tTPt) ILqx,,/( qy ⋅ Lz) (9)

At the lef hand side (Lz ⋅ tPt) is the area where the electric current fows. At the right hand side (Lq,y ⋅ Lz) is the area of the thermal contact and corresponds to the region where the spin Seebeck efect rises. Te previous relation can be simplifed, leading to Eq. (1) and permitting a direct test of the reciprocity by using the experimental values. By taking the average temperature T = (298 ± 2) K, the spin Seebeck experiment gives

ΔVey, T =.(6 30±.3) × 10−−31KA Iqx, (10) which is in excellent agreement with the spin Peltier value of Eq. (3) and verifes experimentally the reciprocal relation, Eq. (1), between spin Seebeck and spin Peltier efects. Once the reciprocity is verifed, we can take the second equal sign of Eq. (8) and obtain an experimental value that can be compared with the theoretical coefcients. By labeling the value taken from equation (8) as KYIG/Pt we fnd from the experiments

−−16 21 KYIG/Pt =.(4 00±.3) × 10 mA (11) We now compare the obtained value with the coefcients known from the literature. For what concerns the spin Hall angle we choose the absolute value of 0.1, similar to what was found experimentally47,48 on samples of 49 YIG with Pt layers of comparable thickness . In this work we use the spin Hall angle θSH for the current of magnetic moments which has opposite sign with respect to the one for spin currents reported in the literature (i.e. we 21,22 have negative θSH for Pt and positive for W and Ta) . By using μ0σYIG = vYIGlYIG and employing the values of the 21 −2 −1 coefcients determined in previous works (εYIG  −10 TK and θSH = −0.1) we can quantify the only miss- ing parameter, vp/vYIG, as vpY/9v IG  . Tis value is compatible with the transmission of the magnetic moment current between the two layers as determined by the intrinsic difusion lengths lM, by the thicknesses t and by the 22 intrinsic conductances vM of YIG and Pt. By using the expression for vp with lPt  73. nm and lYIG ~ 04. μm and with vYIGP~ v t we obtain vp/vYIG = 8 which is reasonably close to the measured value. We are therefore able to evaluate the cooling potentiality of the spin Peltier efect. If we consider the YIG/Pt device able to operate in adiabatic conditions (Iq,c = 0), the temperature change across the device ΔT will be

Δ=TTΔ−SP YIG,Iq JH (12)

where we have assumed Pt  YIG and   YIG. By taking the specifc device studied in this paper, the electric current which is maximizing ΔT is Ie,y = −12.4 μA giving a maximum temperature change of ΔT = 3.8 × 10−8 K. Tis value appears so small to discourage any attempt to employ the SPE in practice. However the verifcation of the validity of the thermodynamic theory for the SPE and SSE (Eq. (8)) ofers, in future per- spective, the possibility to design and optimize spin Peltier coolers and spin Seebeck generators going beyond the specifc bilayer sample used in this experimental study. Work is in progress along this line, however two main preliminary comments are already possible at this stage. Te frst is to identify the YIG and Pt thicknesses that would optimize the efects. Te answer comes from the fact that both materials are active over a thickness of the order of the difusion length lM. Terefore promising devices would have tYIGY~ l IG and tPt ~ lPt. Te second is ζ = εσ2 κ that, as for thermoelectrics, the thermomagnetic YIG is characterized by a fgure of merit T YIG YIGYT/ IG, ζ × −3 22 ζ which is indeed very small at room temperature, T  410 . However it is expected that the T parameter could improve in the temperature range between 50 and 100 K where experiments50 have reported a much larger SSE (almost a factor 5) than the room temperature value. Finally it is worth to mention that both improvements 51 ζ ~ could further beneft by cascading several devices in thermal series . For example, with T 1 and using a mul- tilayer with an appropriate compensation of the Joule heat of each layer by using variable cross sections, one could

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obtain up to an efective ΔT = 20 K for a device containing ~103 junctions. Work along this line has already pro- gressed and future improvements are expected19. In summary, we investigated experimentally both the SPE and the SSE in a bulk YIG/Pt device. Te thermal observables of these experiments are investigated by means of heat current measurements. Tis introduces a novel technique for the SPE characterization of a given sample in the DC regime. Te experimental results of the SPE and SSE are used to verify for the frst time the reciprocal relation between the two. Te relation between both efects with the intrinsic and extrinsic parameters of YIG and Pt bilayer ofers the possibilities for a more in-depth investigation of the applicability of spincaloritronic devices. Methods Device and experimental setup. Te YIG/Pt device employed is made of a bulk yttrium iron garnet (YIG) single crystal prepared by crystal growth in high-temperature solutions applying the slow cooling method52. Single crystals which nucleate spontaneously at the crucible bottom and grow to several centimetres sizes have been separated from the solution by pouring out the residual liquid. Aferwards, one crystal was cut parallel to one of its facets to prepare slices and parallelepipeds of the following dimensions: Ly = 4.95 mm, Lz = 3.91 mm, tYIG = 0.545 mm. Carefully grinding and polishing result in a sample with optical smooth surfaces (Rq = 0.4 nm obtained by AFM). Afer polishing both sides, a thin flm of Pt (tPt about 5 nm) was sputtered on the top of one of the Ly × Lz surfaces at University of Loughborough (United Kingdom). Subsequently two 100 nm thick gold electrode strips for electric contacts were deposited. Te inner distance between the electrodes is equal to Le,y = 4.17 mm. Te Au contacts on the Pt layer are electrically connected to 40 μm diameter platinum leads by silver paste. Te SSE voltage is measured by means of a Keithley 2182 nanovoltmeter while the SPE electric current is generated by a Keithley 2601 source meter. In order to avoid heat leakages all measurements are performed under vacuum (1.6 × 10−4 mbar) by means of a turbomolecular pump. Te heat current sensors are miniaturized Peltier cells (5 × 5 mm and 1.9 mm of thickness, RMT Ltd model 1MD04-031-08TEG), calibrated according to the procedure described in ref.24. Te char- acteristic Iq = −SpVp of both heat sensors are described by Sp = 0.97 ± 0.01 V/W, where Iq is the heat current traversing the sensor and Vp is the voltage measured by a nanovoltmeter. Te thermal reservoirs are two brass parallelepipeds (1 × 1 × 2 cm) to which one face of each heat sensor is glued with silver paste. Te other face of each sensor is clamping the YIG/Pt device. We use an aluminum nitride slab (3 × 3 × 4 mm) with a large nominal thermal conductivity (140–180 Wm−1 K−1) as geometrical adapter to thermally connect the Pt side of the device with the corresponding heat sensor. Tin layers of silicon based thermal grease are used to ensure uniform thermal conductivity through the sections.

Ofset subtractions during SPE and SSE measurements. In the case of the electric current inversion method, the spin Peltier heat signals is afected by a spurious heat current ofset, Iq,of, (a few percent of the total) that is not present in the magnetic feld inversion method and should be therefore subtracted. Te reason for this spurious heat current ofset is that a conventional Peltier efect arises in presence of diferent metal contacts in the measurement setup (i.e. the contact between Pt and Au layers and the contacts with the electrical leads). Tese contacts would give a transverse (along y) heat fux, however the presence of an even very small transverse heat leakage may contribute to a small longitudinal contribution. Tis spurious conventional Peltier efect Iq,of presents, with respect to the current inversion, the same odd parity as the spin Peltier signal. When using the odd parity of the SPE under magnetic feld inversion the spurious efect is cancelled. Conversely, when determining the SPE through the electric current inversion ±Ie,y method, it is summed up. Te ofset is subtracted by using one measurement with magnetic feld inversion method at saturation as a reference. Also the spin Seebeck experiment is afected by a spurious voltage measured at Pt which is the reciprocal of the one found in the spin Peltier with current inversion. A very small transverse leaking heat fux may gives rise to electric efects in the nV range caused by the ordinary Seebeck efect due to the electric contacts between diferent metals. Again, this ofset voltage is eliminated by using one magnetic feld inversion point at saturation as a reference. Data Availability All data generated or analysed during this study are included in this published article (and its Supplementary Information fles). References 1. Callen, H. B. Termodynamics and an introduction to Termostatistics (John Wiley and Sons, New York, 1985). 2. Miller, D. G. Termodynamics of irreversible processes. Te experimental verifcation of the Onsager reciprocal relations. Chemical Reviews 60, 15–37 (1960). 3. Goldsmid, H. J., Nolas, G. S. & Sharp, J. Termoelectrics: basic principles and new materials development (Springer, Berlin, 2001). 4. Onsager, L. Reciprocal relations in irreversible processes. I. Physical Review 37, 405 (1931). 5. Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics. Nature materials 391, 11 (2012). 6. Boona, S. R., Myers, R. C. & Heremans, J. P. Spin caloritronics. Energy Environ. Sci. 7, 885 (2014). 7. Yu, H., Brechet, S. D. & Ansermet, J.-P. Spin caloritronics, origin and outlook. Physics Letters A 381, 825–837 (2017). 8. Ansermet, J.-P. Spintronics: Conceptual building blocks. In et al., E. B. (ed.) Magnetism and Synchrotron Radiation, Proceedings in Physics 133, 43 (Springer, 2010). 9. Yu, X.-Q., Zhu, Z.-G., Su, G. & Jauho, A.-P. Spin-caloritronic batteries. Phys. Rev. Applied 8, 054038 (2017). 10. Martin-Gonzalez, M., Caballero-Calero, O. & Diaz-Chao, P. Nanoengineering thermoelectrics for 21st century: Energy harvesting and other trends in the feld. Renewable and Sustainable Energy Reviews 24, 288 (2013). 11. Uchida, K. et al. Termoelectric generation based on spin Seebeck efects. Proceedings of the IEEE 104, 1946 (2016). 12. Dejene, F., Flipse, J. & van Wees, B. Verifcation of the Tomson-Onsager reciprocity relation for spin caloritronics. Physical Review B 90, 180402 (2014). 13. Flipse, J. et al. Observation of the spin Peltier efect for magnetic insulators. Physical Review Letters 113, 027601 (2014). 14. Uchida, K. et al. Spin Seebeck insulator. Nature Materials 9, 894 (2010).

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15. Uchida, K. et al. Observation of longitudinal spin-Seebeck efect in magnetic insulators. Appl. Phys. Lett. 97, 172505 (2010). 16. Uchida, K. et al. Longitudinal spin Seebeck efect: from fundamentals to applications. Journal of Physics: Condensed Matter 26, 343202 (2014). 17. Daimon, S., Uchida, K.-I., Iguchi, R., Hioki, T. & Saitoh, E. Termographic measurements of the spin Peltier efect in metal/yttrium- iron-garnet junction systems. Phys. Rev. B 96, 024424 (2017). 18. Daimon, S., Iguchi, R., Hioki, T., Saitoh, E. & Uchida, K. Termal imaging of spin Peltier efect. Nature communications 7, 13754 (2016). 19. Uchida, K. et al. Enhancement of the spin Peltier efect in multilayers. Phys. Rev. B 95, 184437 (2017). 20. Itoh, R. et al. Magnetic-feld-induced decrease of the spin Peltier efect in Pt/Y3Fe5O12 system at room temperature. Phys. Rev. B 96, 184422 (2017). 21. Basso, V. et al. Nonequilibrium thermodynamics of the spin Seebeck and spin Peltier efects. Phys. Rev. B 93, 184421 (2016). 22. Basso, V., Kuepferling, M., Sola, A., Ansalone, P. & Pasquale, M. Te spin Seebeck and spin Peltier reciprocal relation. IEEE Magnetics Letters (2018). 23. Sola, A. et al. Evaluation of thermal gradients in longitudinal spin Seebeck efect measurements. J. Appl. Phys. 117, 17C510 (2015). 24. Sola, A. et al. Longitudinal spin Seebeck coefcient: heat fux vs. temperature diference method. Scientifc reports 7, 46752 (2017). 25. Bougiatioti, P. et al. Quantitative disentanglement of the spin Seebeck, proximity-induced, and ferromagnetic-induced anomalous Nernst efect in normal-metal–ferromagnet bilayers. Physical review letters 119, 227205 (2017). 26. Prakash, A. et al. Evidence for the role of the magnon energy relaxation length in the spin Seebeck efect. Physical Review B 97, 020408 (2018). 27. Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall efects. Rev. Mod. Phys. 87, 1213–1260 (2015). 28. Rezende, S. M., Rodriguez-Suarez, R. L., Cunha, R. O., Ortiz, J. C. L. & Azevedo, A. Bulk magnon spin current theory for the longitudinal spin Seebeck efect. Journal of Magnetism and Magnetic Materials 400, 171–177 (2016). 29. Basso, V., Ferraro, E. & Piazzi, M. Termodynamic transport theory of spin waves in ferromagnetic insulators. Phys. Rev. B 94, 144422 (2016). 30. Nakata, K., Simon, P. & Loss, D. Spin currents and magnon dynamics in insulating magnets. Journal of Physics D: Applied Physics 50, 114004 (2017). 31. Uchida, K. et al. Intrinsic surface magnetic anisotropy in Y3Fe5O12 as the origin of low-magnetic-feld behavior of the spin Seebeck efect. Physical Review B 92, 014415 (2015). 32. Hofmeister, A. M. Termal difusivity of garnets at high temperature. Physics and Chemistry of Minerals 33, 45–62 (2006). 33. Uchida, K., Kikkawa, T., Miura, A., Shiomi, J. & Saitoh, E. Quantitative temperature dependence of longitudinal spin Seebeck efect at high temperatures. Phys. Rev. X 4, 041023 (2014). 34. Chotorlishvili, L. et al. Fokker-Planck approach to the theory of the magnon-driven spin Seebeck efect. Phys. Rev. B 88, 144429 (2013). 35. Cunha, R. O., Padron-Hernandez, E., Azevedo, A. & Rezende, S. M. Controlling the relaxation of propagating spin waves in yttrium iron garnet/Pt bilayers with thermal gradients. Phys. Rev. B 87, 184401 (2013). 36. Etesami, S. R., Chotorlishvili, L., Sukhov, A. & Berakdar, J. Longitudinal spin current induced by a temperature gradient in a ferromagnetic insulator. Phys. Rev. B 90, 014410 (2014). 37. Rezende, S. M. et al. Magnon spin-current theory for the longitudinal spin-Seebeck efect. Phys. Rev. B 89, 014416 (2014). 38. Ritzmann, U. et al. Magnetic feld control of the spin Seebeck efect. Phys. Rev. B 92, 174411 (2015). 39. Cornelissen, L. J., Peters, K. J. H., Bauer, G. E. W., Duine, R. A. & van Wees, B. J. Magnon spin transport driven by the magnon chemical potential in a magnetic insulator. Phys. Rev. B 94, 014412 (2016). 40. Geprags, S. et al. Origin of the spin Seebeck efect in compensated ferrimagnets. Nat Commun 7 (2016). 41. Nakata, K., Simon, P. & Loss, D. Wiedemann-Franz law for magnon transport. Phys. Rev. B 92, 134425 (2015). 42. Ohnuma, Y., Matsuo, M. & Maekawa, S. Teory of the spin Peltier efect. Phys. Rev. B 96, 134412 (2017). 43. Saslow, W. M. Irreversible thermodynamics of uniform ferromagnets with spin accumulation: Bulk and interface dynamics. Phys. Rev. B 95, 184407 (2017). 44. Saitoh, E., Ueda, M., Miyajima, H. & Tatara, G. Conversion of spin current into charge current at room temperature: Inverse spin- Hall efect. Appl. Phys. Lett. 88, 182509 (2006). 45. Bender, S. A. & Tserkovnyak, Y. Interfacial spin and heat transfer between metals and magnetic insulators. Phys. Rev. B 91, 140402(R) (2015). 46. Johnson, M. & Silsbee, R. H. Termodynamic analysis of interfacial transport and of the thermomagnetoelectric system. Phys. Rev. B 35, 4959 (1987). 47. Althammer, M. et al. Quantitative study of the spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids. Physical Review B 87, 224401 (2013). 48. Wang, H. L. et al. Scaling of spin Hall angle in 3d, 4d, and 5d metals from Y3Fe5O12/metal spin pumping. Phys. Rev. Lett. 112, 197201 (2014). 49. Hofmann, A. Spin Hall efects in metals. IEEE transactions on magnetics 49, 5172–5193 (2013). 50. Kikkawa, T. et al. Critical suppression of spin Seebeck efect by magnetic felds. Phys. Rev. B 92, 064413 (2015). 51. Ramos, R. et al. Unconventional scaling and signifcant enhancement of the spin Seebeck efect in multilayers. Phys. Rev. B 92, 220407 (2015). 52. Görnert, P. & Voigt, F. High temperature solution growth of garnets: theoretical models and experimental results. Current topics in materials science 11, 1–149 (1984). Acknowledgements We thank Kelly Morrison at the University of Loughborough for the deposition of the Pt flm. We thank Luca Martino and Federica Celegato (from Istituto Nazionale di Ricerca Metrologica) for technical support during the assembling of the measurement system. One author (C.D.) thanks R. Meyer and B. Wenzel for technical support in sample preparation. Author Contributions A.S., V.B., M.K. and M.P. devised the measurement technique and wrote the manuscript. C.D. prepared the YIG sample, A.S. developed the measurement setup and characterized the device, V.B. developed the theoretical model. All authors discussed the results, their physical interpretation and reviewed the manuscript. Additional Information Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-019-38687-4. Competing Interests: Te authors declare no competing interests.

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